SUPPORT for the federal government has inched up to a six-month high and Julia Gillard has edged ahead of Tony Abbott as preferred prime minister but the Coalition would still win in a canter if an election were held today.

The latest Herald/Nielsen poll shows that two months since the carbon price began, the policy remains unpopular but more than half of voters, or 54 per cent, feel it has made no difference.

The poll of 1400 voters was taken from Thursday to Saturday nights, after a tumultuous fortnight of Parliament in which the government reinstated the Pacific solution for asylum seekers and Ms Gillard faced renewed scrutiny about her conduct as an industrial lawyer 17 years ago.

Up by two points ... Labor in the latest Herald/Nielsen poll. Photo: Andrew Meares

The poll finds Labor's primary vote increased 2 percentage points in a month to 32 per cent, while the Coalition's primary vote fell 2 points to 45 per cent. The Greens fell one point to 11 per cent.

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This gives the Coalition a two-party-preferred lead of 54 per cent to 46 per cent, a drop of 4 points but still enough to guarantee a landslide victory if an election were held now.

Ms Gillard and the Opposition Leader, Mr Abbott, now equal each other in terms of unpopularity. Both have an approval rating of 39 per cent and a disapproval rating of 57 per cent.

However, Ms Gillard's rating as preferred prime minister rose 3 points in a month to 46 per cent while Mr Abbott's rating fell 3 points to 45 per cent.

While the asylum seeker policy was controversial and perceived as a backdown, it has strong support with 67 per cent in favour of sending people to Nauru and Manus Island for processing. Voters were evenly split on the announcement to increase Australia's annual refugee intake from 13,750 to 20,000.

The increase in Labor's primary vote is consistent with other modest improvements for the government during the past month in other published polls, all of which have taken the heat off Ms Gillard's leadership.

The Nielsen poll director, John Stirton, said Labor's primary vote had now increased by a total of 6 points during the past three months and that constituted a trend.

Labor's modest resurgence was offset at the weekend by a comfortable victory for the Country Liberal Party in the Northern Territory election.

The end of Labor's 11-year rule in the territory leaves the party in power federally, and in South Australia, Tasmania and the ACT.

Yesterday, Mr Abbott sought to implicate Ms Gillard for the loss, blaming the disruption caused by the suspension last year of the live cattle trade and the introduction of the carbon tax.

Mr Abbott gloated that he had been invited to launch the campaign of the CLP leader and now Chief Minister, Terry Mills, while the Labor leader, Paul Henderson, asked Ms Gillard to stay away.

Federal ministers pointed out that NT Labor had done well in Darwin but had lost the election in expansive rural electorates with a large indigenous vote.

With two-thirds of the vote counted in the 25-seat Parliament, Labor suffered a primary swing against it of 6.5 per cent and was likely to lose three seats to finish with nine. The CLP would pick up three and jumped to 15. The sole independent, Gerry Wood, held his seat.

Federal Labor rejected any role played by the carbon price in the NT poll.

The Herald poll showed 36 per cent supported the carbon price and 59 per cent were opposed - numbers that have barely changed since March last year.

But after two months of the policy, 54 per cent feel the policy has made no difference, 40 per cent feel they are worse off and 3 per cent better off.

In the poll immediately before the policy started on July 1, 37 per cent felt it would make no difference and 51 per cent felt they would be worse off.

The Treasurer, Wayne Swan, demanded yesterday that Mr Abbott apologise for his scare campaign after acknowledging on Saturday that the ''initial impact of the carbon tax may not be absolutely catastrophic''.

Trade Minister Craig Emerson said today that the poll results were encouraging but added that it was for "others" to analyse the results in detail.

"Certainly the trend is a positive one," Dr Emerson told ABC Radio, adding that the Nielsen result comes on top of other, slightly improved poll results for Labor.

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